> On 23 Nov., 22:19, WM <mueck...@rz.fh-augsburg.de> wrote:> > > in any case the limit of my sequence> > > > 01.> > > > 0.1> > > > 010.1> > > > 01.01> > > > 0101.01> > > > 010.101> > > > 01010.101> > > > 0101.0101> > > > ...> >> > has infinitely many digits right to the point as well as left to the> > point.> > This can be proved by attaching pairs 01 of digits always from the> left and from the right side in a symmetrical way:> > 01.> 01.01> 0101.01> 0101.0101> ...> > The overall behaviour of the digits (not of the indices) is the same> as that of the original sequence.> The sequence.01.0101.010101.01010101...has limit 1/99, which is finitely expressible both as a repeating decimal and as a rational number, but that does not mean that either

01.01.010101.010101.0101...

or

01.0.1010.101.010101.01010.10101010.1010101.0101...

has any limit expressible in the positional notation of decimals, or any other such base.--